LLMs for Game Theory: Entropy-Guided In-Context Learning and Adaptive CoT Reasoning
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| Format: | Preprint |
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2026
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| _version_ | 1866915932835676160 |
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| author | Banfi, Tommaso Felice Gamage, Sashenka |
| author_facet | Banfi, Tommaso Felice Gamage, Sashenka |
| contents | We propose a novel LLM-based framework for reasoning in discrete, game-theoretic tasks, illustrated with \emph{Tic-Tac-Toe}. The method integrates in-context learning with entropy-guided chain-of-thought (CoT) reasoning and adaptive context retrieval. The model dynamically adjusts both the number of retrieved examples and reasoning paths according to token-level uncertainty: concise reasoning with minimal context is used when uncertainty is low, whereas higher uncertainty triggers expanded multi-path CoT exploration. Experimental evaluation against a sub-optimal algorithmic opponent shows that entropy-aware adaptive reasoning substantially improves decision quality, increasing the average game outcome from \(-11.6\%\) with the baseline LLM to \(+9.5\%\) with entropy-guided adaptive reasoning over 100 games (win = +1, tie = 0, loss = -1), while maintaining a relatively low number of LLM queries per game. Statistical validation confirms that the improvement is significant, and correlation analysis reveals a negative association between token-level entropy and move optimality. These findings demonstrate that uncertainty-guided adaptive reasoning effectively enhances LLM performance in sequential decision-making environments. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2601_10775 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | LLMs for Game Theory: Entropy-Guided In-Context Learning and Adaptive CoT Reasoning Banfi, Tommaso Felice Gamage, Sashenka Computation and Language Computer Science and Game Theory Machine Learning I.2.7; I.2.6; I.2.4 We propose a novel LLM-based framework for reasoning in discrete, game-theoretic tasks, illustrated with \emph{Tic-Tac-Toe}. The method integrates in-context learning with entropy-guided chain-of-thought (CoT) reasoning and adaptive context retrieval. The model dynamically adjusts both the number of retrieved examples and reasoning paths according to token-level uncertainty: concise reasoning with minimal context is used when uncertainty is low, whereas higher uncertainty triggers expanded multi-path CoT exploration. Experimental evaluation against a sub-optimal algorithmic opponent shows that entropy-aware adaptive reasoning substantially improves decision quality, increasing the average game outcome from \(-11.6\%\) with the baseline LLM to \(+9.5\%\) with entropy-guided adaptive reasoning over 100 games (win = +1, tie = 0, loss = -1), while maintaining a relatively low number of LLM queries per game. Statistical validation confirms that the improvement is significant, and correlation analysis reveals a negative association between token-level entropy and move optimality. These findings demonstrate that uncertainty-guided adaptive reasoning effectively enhances LLM performance in sequential decision-making environments. |
| title | LLMs for Game Theory: Entropy-Guided In-Context Learning and Adaptive CoT Reasoning |
| topic | Computation and Language Computer Science and Game Theory Machine Learning I.2.7; I.2.6; I.2.4 |
| url | https://arxiv.org/abs/2601.10775 |